Find the rectangle with the greatest area, with a corner on O(0,0), one in the Ox axis and one on Oy axis, and one on the parabolic curve $y=4-x^2$ I thought to use the tangent of the parabolic function f'(x)=-2x. i don't know what to do next. For sides a and b the area is S=a*b
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What's the area of the rectangle for any x,y? – Kaynex Nov 18 '16 at 15:52
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You need to create a formula for the area of the rectangle in just one variable, $x$. Then you can maximize that function by taking the first derivative. – turkeyhundt Nov 18 '16 at 15:53
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The opposite corner of $O(0,0)$ can be written as $P(t,4-t^2)$
So, we need to maximize $$f(t)=t(4-t^2)$$
lab bhattacharjee
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You're right, it has something to do with derivatives, but you can't just scan the problem and look for the first function you see, and take the derivative of it.
This is an optimization problem, and we know that because of the word highest (it should probably be greatest). Greatest what? Greatest area. So construct the function that computes the area of the rectangle. That is the function you want to take the derivative of.
Matthew Leingang
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I know I have to take the derivative of the function I get. The problem is that I can't find the function of the area – prishila Nov 18 '16 at 16:05
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@prishila: The figure is a rectangle. What are its dimensions (width and height)? How do you find the area from the dimensions? – Matthew Leingang Nov 18 '16 at 16:14